The dateplot library shipped with pgfplots cannot handle seconds due to limited accuracy.
If you need accuracy of this granularity, you can probably ignore the DATE part of your input. In this case, a solution could be as follows:
\documentclass{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{dateplot}
\def\checkSameDate#1{%
\ifnum\coordindex=0
\gdef\itsDate{#1}%
\else
\def\temp{#1}%
\ifx\temp\itsDate
\else
\PackageError{custom}{Sorry, expected the same date but got two different ones \itsDate\space and #1}{}%
\fi
\fi
}%
\def\ensuretwodigits#1{%
\ifnum#1<10
\edef\pgfmathresult{0#1}%
\else
\edef\pgfmathresult{#1}%
\fi
}%
\pgfplotsset{
% invoked with
% 2013-06-03 23:59:00
% ->
% #1 = 2013
% #2 = 06
% #3 = 03
% #4 = 23
% #5 = 59
% #6 = 00
@datetime to number/.code args={#1-#2-#3 #4:#5:#6}{%
\checkSameDate{#1-#2-#3}%
%
% convert to full seconds:
\pgfmathparse{#4*3600+60*#5 + #6}%
},
%
% This is a style which activates the new feature:
date same day in x/.style={%
x coord trafo/.style={/pgfplots/@datetime to number=##1},
scaled x ticks=false,
plot coordinates/math parser=false,
%
% the following keys are ONLY here to format tick labels
x coord inv trafo/.code={%
\begingroup
% compute the value
\pgfkeys{/pgf/fpu}%
%
% ... \seconds
\pgfmathparse{mod(##1,60)}%
\pgfmathfloattoint{\pgfmathresult}%
\ensuretwodigits{\pgfmathresult}%
\global\let\seconds=\pgfmathresult
%
% ... \minutes
\pgfmathparse{mod( (##1 - \seconds)/60,60)}%
\pgfmathfloattoint{\pgfmathresult}%
\ensuretwodigits{\pgfmathresult}%
\global\let\minutes=\pgfmathresult
%
% ... \hours
\pgfmathparse{(##1 - 60*\minutes - \seconds)/3600}%
\pgfmathfloattoint{\pgfmathresult}%
\ensuretwodigits{\pgfmathresult}%
\global\let\hours=\pgfmathresult
\endgroup
},
xticklabel style={
/pgf/number format/fixed,
},
xticklabel=\hours:\minutes:\seconds,
},
}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
%xtick=data,
xticklabel style={anchor=east,rotate=45},
date same day in x,
]
\addplot table [col sep=comma,trim cells=true,y=value1,scatter,only marks] {
date, value1
2013-06-03 23:59:00, 2
2013-06-03 23:59:10, 3
2013-06-03 23:59:20, 3
2013-06-03 23:59:30, 3
2013-06-03 23:59:40, 3
2013-06-03 23:59:50, 14
2013-06-03 23:59:59, 14
};
\end{axis}
\end{tikzpicture}
\end{document}

My idea is to provide a trivial transformation which ignores the DATE part and maps the TIME part to a number. I added a sanity check which verifies that that date part is the same.
EDIT: I added an inverse transformation which allows to format tick labels automatically, even if pgfplots chose the tick positions automatically.
x coord trafo(the inverse trafo is unnecessary if you provide tick labels explicitly anyway). – Christian Feuersänger Jun 11 '13 at 18:25